Related papers: On the classification of Galois objects for finite…
In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We determine the fundamental group of period domains over finite fields.
Let $\mathcal{A}$ be a finite-dimensional algebra over a finite field $\mathbf{F}_q$ and let $G=\mathcal{A}^\times$ be the multiplicative group of $\mathcal{A}$. In this paper, we construct explicitly a generic Galois $G$-extension $S/R$,…
We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to…
We study the structure of abelian subgroups of Galois groups of function fields of surfaces.
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…
If we consider a q-analogue of linear differential equation, Galoois group of the q-analogue difference equation is still a linear algebraic group. Namely, by a quantization of linear differential equation, Galois group is not quantized. We…
For any finite group G and integer i, let $\mathcal{H}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups $\hat{H}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes…
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra…
We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations…
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
This paper extends the study of group algebras of finite groups in which the socle of the center is an ideal. We provide a detailed analysis of the structure of these groups. In a particular case, we reach a complete characterization of the…
We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…
The free profinite product of finitely many absolute Galois group is an absolute Galois group.